Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer}

Determine whether Relation R on the set Z of all integer defined as R={(x ,\ y): (x-y) =i n t e g e r} is reflexive, symmetric or transitive.

Determine whether Relation R on the set N of all natural numbers defined as R={(x ,\ y): y=x+5 and x<4} is reflexive, symmetric or transitive.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Define a relation R on the set N of all natural numbers by R = {(x, y) : y = x + 5, x is a natural number less than 4)

Let R be the relation on the Z of all integers defined by (x ,y) in R x-y is divisible by n . Prove that: (x ,x) in R for all x in Z (x ,y) in R (y ,x) in R for all x ,y in Z (x ,y) in Ra n d(y , z) in R (x ,z) in R for all x ,y ,z in R

The relation R on the set N of all natural numbers defined by (x ,\ y) in RhArrx divides y , for all x ,\ y in N is transitive.

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.